Nozzle Reynolds Number Research Articles

Impingement Calculations for Ultra-Low Density Helium Thrusters

A new semi-empirical thruster plume model is presented based on recent experimental and numerical (Direct Simulation Monte Carlo) studies. The results are unique in that they pertain to unprecedentedly low flow rates (nozzle Reynolds numbers below 200). The model is used in computing the impingement forces acting on a spacecraft solar panel emersed in a thruster plume. The time-varying impingement effects due to changes in surface temperature were found not to be a serious limitation on the thruster calibration accuracies for the GP-B and STEP spacecraft. This suggests that both spacecraft could yield useful aeronomic data through monitoring of the thruster activity of the drag-free control systems.

Impingement of an axisymmetric jet on unheated and heated flat plates

The aerodynamic and thermal aspects of the wall jet flow, formed after angled impingement of an axisymmetric jet, have been studied with emphasis on the large-scale transport of the passive scalar by the spatially coherent structures. Time-averaged and instantaneous structures of the turbulent flow were examined by visualization and local measurements of a jet arrangement with an impingement angle between the jet axis and the surface normal of 20°, a nozzle-to-plate distance to nozzle exit diameter ratio of 22, and a nozzle exit Reynolds number of 1.3 × 104.The results show that the oblique impingement introduced vertical velocities so that boundary-layer approximations were inapplicable and led to the distribution of the time-averaged properties of the velocity and temperature field with strong azimuthal dependence, which increased gradually with angle of impingement to 40° where a sudden change of the orientation of the contours of surface pressure and temperature took place. It also led to instantaneous, spatially coherent structures which were most pronounced at an angle of 20°. These structures improved the large-scale transport of the passive scalar but, owing to the extreme regularity of their path, also led to an inactive zone near the vortex centre.The inner region of the decelerating wall jet exhibited a momentum equilibrium layer extending to the point of radial velocity maximum and the intercept of the linear region of the semilogarithmic wall law varied in the local streamwise direction as for turbulent flows over rough walls with adverse pressure gradient. The thermal equilibrium layer had an invariant functional form but extended far beyond the point of maximum velocity.

On the applicability of various scaling laws to the turbulent wall jet

The spatial distribution of the mean velocity in a two-dimensional turbulent wall jet was measured for a variety of nozzle Reynolds numbers. It was determined that the bulk of the flow is self-similar and it depends on the momentum flux at the nozzle and on the viscosity and density of the fluid. The width of the nozzle which was commonly used to reduce these data has no part in the similarity considerations as has already been suggested by Narasimha et al. (1973). This type of self-similarity can be easily applied to determine the skin friction, which can otherwise only be determined with considerable difficulty. It was also shown that the ‘law of the wall’ applies only to the viscous sublayer. The Reynolds stress in the inviscid, inner portion of the flow is not constant thus the assumption of a ‘constant stress layer’ is not applicable. The applicability and universality of the ‘outer scaling law’ (i.e. Coles’ law of the wake) has been verified throughout the inviscid inner portion of the wall jet. The logarithmic velocity distribution cannot be derived by making the usual assumptions based on the constancy of the Reynolds stresses or on the thinness of the logarithmic region relative to the thickness of the inner layer.

Mass Transfer from an Oblique Impinging Slot Jet

The local mass‐transfer rate of a submerged oblique impinging slot jet has been studied with an electrochemical limiting current technique for the reduction of ferricyanide ion at isolated microelectrodes on the impinged surface. The mass‐transfer rate distributions over a span of surface distances of −24 to 32 nozzle widths from the jet centerline, were determined for the jet angles of 15–90°, nozzle Reynolds numbers of 1000–7000, and nozzle heights of 1–8 nozzle widths. Empirical equations are presented to correlate the local Sherwood numbers at the stagnation point, in the laminar boundary layer and wall jet flow regimes of the impinging jets as functions of the jet angle, nozzle Reynolds number, dimensionless distance from the jet centerline, and dimensionless nozzle height. The root mean square deviation between the empirical equations and 3537 experimental data points was within ± 14.3%.

軸方向ジェットノズルを備えた混合槽内での熱伝達係数及び混合時間

Heat transfer coefficient and mixing time were measured in an axial-jet mixing vessel equipped with a single or combined nozzle of various diameters.The equivalent nozzle diameter de for such a nozzle was defined asde = {(1/2)(4/π)2(pQ3/P)}1/4where Q and P are total jet flow rate and total power input, respectively. The equivalent nozzle diameter was usable for the correlation of heat transfer coefficient and mixing time for the combined jet nozzle.The heat transfer coefficient measured was well correlated with nozzle Reynolds number Ren (≡uedeρ/μ) by using the equivalent nozzle diameter, ashD/κ = 0.27(uedeρ/μ)3/4Pr0.4(μ/μw)0.144.2 × 103 Ren 4The mixing time measured was well correlated with the nozzle Reynolds number, based on the correlation method of Hiby et al. The minimum dimensionless mixing time was obtained at Ren = 1.0 × 104–1.3 × 104, and its value satisfied the correlation equation proposed in our previous paper.

The mechanism of bubble formation through a submerged nozzle in upward water flow.

The theoretical study was carried out to clarify the mechanism of bubble formation through a submerged nozzle in upward water flow. On the basis of the experimental results, a model of breakup of the air column in which the surface membrane is oscillating at the top of the nozzle due to the disturbance of flow was proposed. The size of the bubble generated from a nozzle in a stream ranging from Nozzle Reynolds number 1500 to 15000 was determined by applying the theory of the instability of a jet which was first analyzed by Lord Rayleigh. The proposed model is in good agreement with the experimental results.

Dimensional Analysis of Continuous High-capacity Electrodispersion of Aqueous Based Liquids in an Organic Continuous Phase

Abstract High-intensity electric fields can be used to disperse aqueous-based solutions in a relatively nonconducting immiscible organic phase. Dimensional analysis of electrical dispersion performance from a single grounded nozzle between two charged electrodes can be characterised in terms of five dimensionless groups: an electrode height; nozzle-electrode distance; a nozzle Reynolds number; an electrical Bond number, which relates electrical to surface forces; and a Taylor number, which relates electrical to viscous forces. Experimental results on the electrodispersion of water in 2-ethyl-1-hexanol indicate that pulsed DC fields can accomplish electrodispersion utilizing a lower rms-voltage than steady DC fields. In addition, the pulsed-field-behavior varies with pulse frequency with 200 Hz fields being more effective for higher continuous-phase viscosities while 2000 Hz fields are more effective when the viscosity is lower. A steady DC field displays invariant behavior with changing viscosity. In the ...

Mixing characteristics of urethane based materials and polyurea in RIM

AbstractTo facilitate the study of new reaction injection molding (RIM) materials on a practical scale, a lab‐scale mini‐RIM machine was constructed. This machine is capable of delivering up to approximately 250 cc of material at rates of up to 125 cc/s. The RIM machine was first tested with conventional materials such as crosslinked and linear polyurethanes. The effect of varying the nozzle Reynolds number upon the adiabatic temperature rise corresponded to the results reported in previous works. Following this verification, two developmental materials, a polyurethane/polyester interpenetrating polymer network and a polyurea, were examined. The polyurea material showed a very strong dependency on mixing up to a Reynolds number above 400. The 75/25 PU/PEster reaction exotherms also showed a dependency upon mixing. However, this dependency is noticeable only in the polyester portion of the reaction, which can be attributed to the mixing sensitivity of the redox‐type initiators used.

Vacuum chamber pressure effects on thrust measurements of low Reynolds number nozzles

Tests were conducted to investigate the effect of vacuum facility pressure on the performance of small thruster nozzles. Thrust measurements of two converging-diverging nozzles with an area ratio of 140 and an orifice plate flowing unheated nitrogen and hydrogen were taken over a wide range of vacuum facility pressures and nozzle throat Reynolds numbers. In the Reynolds number range of 2200 to 12,000 there was no discernable viscous effect on thrust below an ambient to total pressure ratio of 1000. In nearly all cases, flow separation occurred at a pressure ratio of about 1000. This was the upper limit for obtaining an accurate thrust measurement for a conical nozzle with an area ratio of 140.

Mass Transfer of a Submerged Jet Impinging on a Cylindrical Surface

The mass transfer rate and wall shear stress for a submerged two‐dimensional slot jet impinging on a convex surface were obtained by measuring the limiting current of the electrochemical reduction of ferricyanide ion. The local mass transfer rate was measured over a range of nozzle Reynolds number (Re) from 2,500 to 13,000, dimensionless nozzle height from 0.2 to 3 and dimensionless radius of curvature from 2 to 6. A relation of was obtained. The value of β was found to be in the impingement region and in the wall jet region.

An analysis using the Chilton—Colburn analogy for mass transfer to a flat surface from an unsubmerged impinging jet

An analysis based on the Chilton—Colburn analogy has been used to correlate the rate of mass transfer to the impingement and boundary layer regimes of an unsubmerged circular impinging jet. The average mass transfer rate on the impinged surface was measured with a limiting current technique for a range of the nozzle Reynolds numbers from 2500 to 20,000, the nozzle height from 0.1 to 5 nozzle diameters and the radius of the active mass transfer area from 0.1 to 5 nozzle diameters. The theoretical correlations agreed well with the present experimental results as well as with the previous literature data.

Effect of curvature on the turbulence of a two-dimensional jet

An experimental study is presented which details the turbulence characteristics of a two dimensional offset jet. A single offset ratio (height of the nozzle above the solid parallel wall by nozzle width) of seven is used with a nozzle Reynolds number of 15,000. Measurements are presented in the preattachment jet region made with a dual frequency shifted laser Doppler anemometer. The relative strain rates resulting from curvature on the upper and lower sides of the jet are determined and their effects on the r. m. s. fluctuating velocity components are presented.

Mass Transfer to a Cylindrical Surface from an Unsubmerged Impinging Jet

The local rate of mass transfer to a convex cylindrical surface from an unsubmerged impinging jet was obtained by measuring the mass‐transfer limiting current of the reduction of ferricyanide ions on a sectioned electrode. The effects of flow rate, nozzle height, and radius of curvature of the impinged surface were investigated. The wall‐shear stress and liquid‐film thickness were also measured. The results indicate that the influence of nozzle height and surface curvature on the local mass transfer rate were relatively minor. The relationship between the local Sherwood number (Sh) and the nozzle Reynolds number (Re) can be expressed aswhere is the nozzle width, and is the surface distance from the point of impingement. The value of exponent β was found to be equal to 0.6 in the impingement regime for and in the wall jet regime for . When the Reynolds number became greater than 6000, the value of β in the wall jet regime increased to . The function was of a polynomial type exhibiting two maxima and one minimum within the range investigated.

Surface phenomena and mass transfer interactions in liquid‐liquid systems

AbstractThe surface dynamics of pendant aqueous droplets forming at a submerged nozzle in an immiscible organic solvent have been studied using a novel laser‐activated photochromic tracer technique. This enabled a small element of surface to be labeled so that its subsequent history could be recorded photographically.Results for aqueous droplets forming in toluene in the absence of any mass transfer indicated only a slow interfacial circulation from the front to the rear, and there was no indication of any surface renewal as a result of hydrodynamic flow even at nozzle Reynolds numbers as high as 300. By contrast, the introduction of any one of a number of organic solutes into the toluene phase led to sporadic Marangoni‐type interfacial disturbances, which in turn resulted in rapid replacement of elements of the droplet surface. It is proposed that renewal of the droplet surface is dependent on solute diffusion in the present instance and that the processes of surface renewal and mass transfer are likely to be interactive.

A novel virtual impactor: Calibration and use

Aerosol separation characteristics of two prototype single-stage virtual impactors are described. Data indicate that the efficiency curve and the 50% cut-off Stokes number ( Stk 50) (or cut-off size) are not sensitive to the nozzle Reynolds number ( Re), and can be predicted as long as the corresponding Re is between 1000 and 8000, the ratio of nozzle to probe distance ( S) to the nozzle diameter ( W) is about 1, and the ratio of the hole diameter ( D 1) to W is between 1.2 and 1.5. The results, however, show that the cut-off sizes are strongly affected by the ratio of minor flow rate ( Q m ) to the total flow rate ( Q T ). Also, the efficiency data reveal that Stk 50 of the liquid dioctyl phthalate aerosol is smaller than that of solid polystyrene Latex aerosol, suggesting internal circulation in the liquid particles at the acceleration nozzle exists. In addition, we found that, near the cut-off particle size, there were substantial losses (20 ∼ 40%) on the surface of the collection probe. The results also show that only parameters D 1/ W and Q m / Q T have a slight effect on the shape of the efficiency curve.

Distribution of striation thickness from impingement mixers in reaction injection molding

AbstractThe striation thickness distribution developed in an impingment T‐mixer is predicted using the statistical theory of turbulent diffusion. The predicted distribution is independent of the mixing nozzle Reynolds number, in agreement with some experiments, and is primarily a function of the mixing head geometry, the ratio of the reagent flow rates and the residence time distribution of the flow in the mixing head. Mixing is described as the result of fluid deformation in the intertial subrange of turbulent flow. The relationship of deformation to time and energy dissipation rate ϵ is examined. In the impingement T‐mixer ϵ is related to the kinetic energies of the streams entering and leaving the head. (There are no surface tension effects and pressure is relatively uniform in the mixing head, so that the kinetic energy is dissipated by viscous forces.) The distribution of residence times of fluid elements in the T‐mixer is responsible for varying degrees of deformation and hence a distribution of striation thickness. This residence time distribution does not seem to have been studied and the flow pattern was thus modeled as perfect macromixing, having an exponential distribution. The procedure developed in this paper to calculate the distribution of striation thickness allows reasonable estimates of its parameters from fluid mechanical information and showed good agreement with experimental values, without having to fit any quantities. This new approach to striation thickness distribution is worth further evaluation.

The effect of electric fields on the absorption of pure sulfur dioxide by water drops

The effect of an electric field on the absorption of sulfur dioxide by pure water drops is examined experimentally. Field strength is varied up to 8.0 kV/cm, and nozzle Reynolds number is varied between 26 and 78. Drop surface charge density, size, shape, shape oscillation, acceleration and total sulfur dioxide uptake are measured directly. Significant reduction in drop size and increase in acceleration with increasing field strength are the major effects observed, while alteration in drop shape and oscillation are slight. Calculated average mass transfer coefficients increase with both field strength and nozzle velocity, but total sulfur dioxide uptake decreases with field strength due to reductions in drop-gas contact time. The results suggest that the design of scrubbers with electric fields concentrated in the region of drop formation but absent elsewhere show the greatest promise for improved efficiency.

Reattachment Flow Issuing from a Finite Width Nozzle : Report 4. Effects of Aspect Ratio of the Nozzle

From the experimental results of a reattachment flow issuing from a finite width nozzle having various aspect ratios, it is made clear that behaviour of the flow is influenced by nozzle shape, Reynolds number and initial turbulence intensity. As aspect ratio of the nozzle becomes smaller than 3, behaviour of the flow changes considerably, influenced by the side plates. The calculated results for a two-dimensional reattachment flow are not valid for such a flow. A new correction factor is introduced as a function of aspect ratio, offset ratio and Reynolds number. As the result, the reattachment distance of a flow having a small aspect ratio can be expressed by using this factor in a wide range of offset ratios, except very small ones.

Aerodynamic levitation of laser-heated solids in gas jets

Solid spheres were aerodynamically levitated in gas jets and laser heated to temperatures above 2000 K. Stable levitation in a supersonic jet from a 0.081-cm nozzle was demonstrated with 0.03–0.20 g, 0.24–0.47-cm-diam specimens at a height between 0.7–2.0 cm above the nozzle and ambient pressures between 1.1–18 Torr. A model of supersonic jet levitation accurately predicts height vs pressure over the full range of conditions that were investigated. The efficiency with which jet momentum is converted into levitation force decreases with the jet:specimen diameter ratio and jet Reynolds number. The rate of jet spreading with distance from the nozzle deduced from levitation experiments agrees with that measured by pitot tube traverses of the jet. Pitot tube pressure measurements also reveal a transition from laminar to turbulent supersonic jet flow at nozzle Reynolds numbers just above the maximum values at which stable levitation is observed. Laser heating reduces the jet momentum required for levitation at a given height and increases levitation stability. In experiments with subsonic jets, the required jet momentum flow rate exceeds the specimen weight by ∼2/CD, where CD is the specimen drag coefficient at its terminal free-fall speed under the ambient conditions. Exploratory studies of laser-heated liquid levitation are also reported.

The influence of impingement mixing on striation thickness distribution and properties in fast polyurethane polymerization

AbstractImpingement mixing in a polyether polyol/butanediol/MDI, thermoplastic urethane system was evaluated using measurements of striation thickness distribution, adiabatic temperature rise, and molecular weight. Adiabatic temperature rise was less sensitive to mixing quality for this system than for the crosslinking ones previously studied. The average of the distribution of striation thickness as measured by optical microscopy on the resultant polymer decreased with increasing nozzle Reynolds numbers, Re. Molecular weight increased and its polydispersity decreased with increasing Re. Morphological data indicate better phase separation in the poorly mixed samples. These results are consistent with relatively slow diffusion for the polyol and thus the preferential formation of unattached hard segments at lower Re.